Definition:Trivial Category

Definition

The following categories can be seen described as trivial:

Zero Catgegory

The category $\mathbf 0$, zero, is the empty category:

$\qquad$

with:

no objects

and consequently:

no morphisms.

One Category

The category one $\mathbf 1$, is the category with:

Objects:		One object: $*$
Morphisms:		One morphism: the identity morphism $\operatorname{id}_*$.

Discrete Category

Let $\CC$ be a metacategory.

Then $\CC$ is said to be discrete if and only if it comprises only identity morphisms.

If the collection $\CC$ constitutes the objects of $\mathbf C$, then $\mathbf C$ may also be denoted $\map {\mathbf {Dis} } \CC$.

Also see

• Definition:Trivial